Computer graphics processing and selective visual display system – Computer graphics processing – Attributes
Reexamination Certificate
2001-08-21
2004-08-24
Razavi, Michael (Department: 2672)
Computer graphics processing and selective visual display system
Computer graphics processing
Attributes
C345S426000, C345S606000, C345S607000, C382S162000
Reexamination Certificate
active
06781594
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates generally to computer generated images and more particularly to a method for computing the intensity of specularly reflected light.
2. Description of the Background Art
The illumination of a computer-generated object by colored light sources and ambient light is described by an illumination model. The illumination model is a mathematical expression including ambient, diffuse, and specular illumination terms. The object is illuminated by the reflection of ambient light and the reflection of light source light from the surface of the object. Therefore, the illumination of the object is composed of ambient, diffuse, and specularly reflected light. Given ambient light and light sources positioned about the object, the illumination model defines the reflection properties of the object. The illumination model is considered to be accurate if the illuminated object appears realistic to an observer. Typically, the illumination model is incorporated in a program executed by a rendering engine, a vector processing unit, or a central processing unit (CPU). The program must be capable of computing the illumination of the object when the light sources change position with respect to the object, or when the observer views the illuminated object from a different angle, or when the object is rotated. Furthermore, an efficient illumination model is needed for the program to compute the illumination in real-time, for example, if the object is rotating. Therefore, it is desired to incorporate terms in the illumination model that are computationally cost effective, while at the same time generating an image of the illuminated object that is aesthetically pleasing to the observer.
Ambient light is generalized lighting not attributable to direct light rays from a specific light source. In the physical world, for example, ambient light is generated in a room by multiple reflections of overhead florescent light by the walls and objects in the room, providing an omni-directional distribution of light. The illumination of the object by ambient light is a function of the color of the ambient light and the reflection properties of the object.
The illumination of the object by diffuse and specular light depends upon the colors of the light sources, positions of the light sources, the reflection properties of the object, the orientation of the object, and the position of the observer. Source light is reflected diffusely from a point on the object's surface when the surface is rough, scattering light in all directions. Typically, the surface is considered rough when the scale length of the surface roughness is approximately the same or greater than the wavelength of the source light.
FIG. 1A
illustrates diffuse reflection from an object's surface. A light ray i
105
from a source
110
is incident upon a surface
115
at point P
120
, where a bold character denotes a vector. Light ray i
105
is scattered diffusely about point P
120
into a plurality of light rays r
1
125
, r
2
125
, r
3
125
, r
4
125
, and r
5
125
.
If the scale length of the surface roughness is much less than the wavelength of the source light, then the surface is considered smooth, and light is specularly reflected. Specularly reflected light is not scattered omni-directionally about a point on the object's surface, but instead is reflected in a preferred direction.
FIG. 1B
illustrates specular reflection from an object's surface. A light ray i
130
from a source
135
is incident upon a surface
140
at a point P
145
. Light ray i
130
is specularly reflected about point P
145
into a plurality of light rays r
1
150
, r
2
150
, r
3
150
, r
4
150
, and r
155
, confined within a cone
160
subtended by angle &phgr;
165
. Light ray r
155
is the preferred direction for specular reflection. That is, the intensity of specularly reflected light has a maximum along light ray r
155
. As discussed further below in conjunction with
FIGS. 2A-2B
, the direction of preferred light ray r
155
is specified when the angle of reflection is equal to the angle of incidence.
Typically, objects reflect light diffusely and specularly, and in order to generate a realistic illumination of the computer-generated object that closely resembles the real physical object, both diffuse and specular reflections need to be considered.
FIG. 2A
illustrates specular reflection from an object's surface in a preferred direction, including a unit vector l
205
pointing towards a light source
210
, a unit vector n
215
normal to a surface
220
at a point of reflection P
225
, a unit vector r
230
pointing in the preferred reflected light direction, a unit vector v
235
pointing towards an observer
240
, an angle of incidence &thgr;
i
245
subtended by the unit vector l
205
and the unit vector n
215
, an angle of reflection &thgr;
r
250
subtended by unit vector n
215
and the unit vector r
230
, and an angle &thgr;
rv
255
subtended by unit vector r
230
and unit vector v
235
. Light from the source
210
propagates in the direction of a unit vector −l
260
, and is specularly reflected from the surface
220
at point P
225
. A unit vector is a vector of unit magnitude.
Reflection of light from a perfectly smooth surface obeys Snell's law. Snell's law states that the angle of incidence &thgr;
i
245
is equal to the angle of reflection &thgr;
r
250
. If surface
220
is a perfectly smooth surface, light from source
210
directed along the unit vector −l
260
at an angle of incidence &thgr;
i
245
is reflected at point P
225
along unit vector r
230
at an angle of reflection &thgr;
r
250
, where &thgr;
i
=&thgr;
r
. Consequently, if surface
220
is a perfectly smooth surface, then light directed along −l
260
from source
210
and specularly reflected at point P
225
would not be detected by observer
240
, since specularly reflected light is directed only along unit vector r
230
. However, a surface is never perfectly smooth, and light directed along −l
260
from source
210
and specularly reflected at point P
225
has a distribution about unit vector r
230
, where unit vector r
230
points in the preferred direction of specularly reflected light. The preferred direction is specified by equating the angle of incidence &thgr;
i
245
with the angle of reflection &thgr;
r
250
. In other words, specular reflection intensity as measured by observer
240
is a function of angle &thgr;
rv
255
, having a maximum reflection intensity when &thgr;
rv
=0 and decreasing as &thgr;
rv
255
increases. That is, observer
240
viewing point P
225
of the surface
220
detects a maximum in the specular reflection intensity when unit vector v
235
is co-linear with unit vector r
230
, but as observer
240
changes position and angle &thgr;
rv
235
increases, observer
240
detects decreasing specular reflection intensities.
A first prior art method for computing the intensity of specularly reflected light is to represent the specular intensity as f(r,v,n)∝(r·v)
n
, where 1≦n≦∞ and n is a parameter that describes the shininess of the object. Since r and v are unit vectors, the dot product r·v=cos &thgr;
rv
, and therefore, f(r,v,n)∝ cos
n
&thgr;
rv
.
A second prior art method computes the intensity of specularly reflected light in an alternate manner. For example,
FIG. 2B
illustrates another embodiment of specular reflection from an object's surface in a preferred direction, including a unit vector l
265
pointing towards a light source
270
, a unit vector n
275
normal to a surface
280
at a point of reflection P
282
, a unit vector r
284
pointing in the preferred reflected light direction, a unit vector v
286
pointing towards an observer
288
, a unit vector h
290
bisecting the angle subtended by the unit vector l
265
and the unit vector v
286
, an angle of incidence &thgr;
i
294
, an angle of reflection &thgr;
r
290
, and an
Carr & Ferrell LLP
Chung Daniel
Razavi Michael
Sony Computer Entertainment America Inc.
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